Ch. 4.4 Factor Quadratic Equation I can find common binomial factors of quadratic expression with lead coefficient of 1

Success Criteria: Factor ax2 + bx + c when a is ±1 Find common Factors

Today’s Agenda Do Now Check HW Lesson Assignment

Do Now: On a suspension bridge, the roadway is hung from cables hanging between support towers. The cable of one bridge is in the shape of the parabola y = 0.1x2 7x + 150, where y is the height in feet of the cable above the roadway at the distance x feet from a support tower.

a. What is the closest the cable comes to the roadway?b. How far from the support tower does this occur?

Factoring Trinomials x + bx + cPositive b and c

Ex 1. x2 + 10x + 24

( )( )

2

Trinomials can factor into 2 binomials.

When the lead coefficient is 1, the first terms are the square root of the variable.x x

1. The signs are determined byterm c. If c is positive the signs are the same.

2. Then look at the sign of the b term, if it is (-) they are both (-). If it is (+) then both signs are (+).

+ +

Factoring Trinomials x + bx + cPositive b and c

Ex 1. x2 + 10x + 24

( )( )

2

x x+ +

3. Determine the factors of c.

241 242 123 84 6

4. Because the signs are the same we add the factors together to find the middlevalue. These are the factorsof the trinomial

6 4

Practice

A. x2 + 5x + 6

B. -x2 - 13x - 30

C. x2 + 20x + 75

D. x2 + 7x + 5

Factoring Trinomials x - bx + cnegative b and positive c

2

Ex 2. x2 - 13x + 22

( )( )

1. Look at sign for c.(positive means same sign)

x x- - 2. Look at the sign for b (-). Then they are both (-).

3. Factor c 22 1 22 2 11

4. What factors are the sum of b?

2 11

Practice

A. x2 - 5x + 4

B. x2 - 15x + 36

C. x2 - 18x + 45

D. -x2 + 7x - 12

Factoring Trinomials x2 - bx - c with negative c

Ex 3 x2 - 8x – 20

( )( )x x

1. Look at sign for c.(negative means opposite signs)

+ -2. Find the factors of c. 20 1 20 2 10 4 5

3. Since signs are oppositeyou must subtract factorsto find the middle term. Keep the signs with the terms.

2 10

Practice

A. -x2 + 5x + 14

B. x2 - 5x - 36

C. x2 + 18x - 40

D. x2 + 18x - 40